Showing posts with label Leverage. Show all posts
Showing posts with label Leverage. Show all posts

Thursday, July 19, 2007

Fantasy Girl Revist - Google Googlplexed

In the fall I was writing my blog over on Stockhouse and I wrote this 10 part series which I titled Fantasy Girl and a subtitle for each post. Half the posts were taking detailed look at why Google's earnings would not keep up, as in the news story Google's Profit Falls Short, Shares Drop. The other half were looking at Goldcorp and the serious valuation problems with that one for investors. Those parts I worked on polishing up further and turned it into my post, How I Discovered the Gold Bubble.

For the Google related part of the series I intended my posts to show how when growth rates are unreasonable large applying that PEG dogma is nonsense by starting with an absurd rate of interest and hoped people would make the connected that their expectations from Google were also absurd.

I like Google's products and services and use the all the time, however, when too many people get on a boat it sinks. Here's my original analysis of Google from November 2006.

Fantasy Girl - Up 10,000,000,000 % Part I

Have you ever had a day where you could say you were up 10,000,000,000%?

Are you sure?

Just what kind of daily percent would you have to make each trading day to make 10,000,000,000% in a year?


Compounding interest is a wonderful thing. I do this math thing where my spreadsheet calculates my percent change for the day, and my annualize change if I did that percent each of the 240 trading days of the year.

The formula if you let D be your day's earnings, O be your day's open is:

Annualized rate of return = (1 + D/O)^240 - 1

The D/O gives you your percent increase for the day, and taking it to the power of 240 compounds it much the same way you might to a simply compounding interest calculation for 10 years.

So, what percent?

Well, I found out yesterday, and wow, what a lesson on compounding interest. 10 billion percent it said, and I went to correct my error, only there wasn't an error. At that point my portfolio was up 8%, and wow, the annualized rate of return if you could do that everyday is 10 billion percent! And a different stock, with a small holding, went up, so I changed it, and wow, up 13 billion %, and up more, and then 33 billion %.

But wait, that's not a lot of extra dollars causing that jump. Huh? I looked at the percents, 8.1% gets you 13 billion, and 8.5% gets you 33 billion, and well, 10.1% gets you over a trillion %.

In absolute terms, the increases are small compared to compounding effects. By comparison, to go from 0%, to 0.1%, the same absolute difference, as 8% to 8.1% the annualized rate goes from zero to 27%, a small percentage difference compared to from 10 billion to 13 billion %.

And herein lies part of the problem in how we can get ourselves into enormous trouble with our portfolio when past growth rates of a company are used to project future valuation. The bigger the growth, the company experienced, ie, already had, the harder it is to ever meet that crazy expectation.

In the next few posts I'll examine the financial difference between using past growth numbers and future growth numbers, and how some of the those past growth numbers are setting investors up for financial ruin.


Fantasy Girl - 300 Billion! Part II

The main idea from the first post in the first Fantasy Girl series was that as the rate gets higher, the magnitude of the difference in compounding increases dramatically with tiny increases in the rate use. The two examples have a mere 0.1% difference in rate. Compounded rate = (1 + daily rate)^240 - 1


Daily rate
Compounded rate
A
8% 10,000,000,000%
B
8.1% 13,000,000,000%
B minus A
0.1% 3,000,000,000%
C
0.0% 0%
D
0.1% 27%
D minus C
0.1%
27%

The tiny increase in rate in these two examples is 0.1%, but the absolute difference becomes unimaginable as the rate gets absurd.

But, what would happen if you did that 0.1% per trading day for say, 12 years?

Year Total interest
0 0%
1
27%
2
62%
3
105%
4
161%
5
232%
6
322%
7
436%
8
581%
9
766%
10
1001%
11
1299%
12
1679%

Well, if you started with $10,000, in 12 years you'd have $177,88, and $167,880 of "wealth" has been created.

But, just how did that wealth get created?

There are many paths to that wealth. Some will create wealth that will be sustainable, and some could be described as lying in wait for nuclear melt down.

How about taking a look at say ... Google (GOOG), and later, a much smaller company.

Google's market cap is $153 billion dollars. Google's share price is up about 33% in two months. About $38 billion dollars of market cap.

And just what is the annualized rate of growth if you increase by 1/3rd in 3 months?

(1.33^6 -1) = 213%

Oh boy, if we keep going like this, we should see $1100/share by next summer and a market of $300 billion. What a great company... And wow, this company is everywhere, it can do anything...

But....

Part III a closer look at what Google's financials are saying...


Fantasy Girl - Googlplex 10^100^10 - Part III

Googolplex - 1 followed by a googol of zeros

Recap:
  • As growth rates increase even marginally, they have exceptionally larger effect on the end numbers.
  • Google has a market cap of $153 billion and its share price is up 33% in two months, creating $38 billion of market cap.
  • To continue at the current growth rate, Google would be up 210% by the end of the year.
Oct 19, 2006
EXTRA, EXTRA READ ALL ABOUT IT

Google Revenues increase 70%

The PEG Ratio says that if price/earning is less than the growth rate, you've got an undervalued stock, although the Motley Fool suggests it should be 0.5 or less to be undervalued (http://www.fool.com/Pegulator/pegulator.htm). For correct use, the PEG is dependent on an expectation of 5 years of growth at the rate used for the earnings per share.

So, just what have Google's earnings per share been?


Quarter
Earnings/ share
1% increase over last Quarter
2Annualized Quarter Growth
3Annual Growth to Q1/05
Q1 2005
1.29n/a
n/a
n/a
Q2 2005
1.19
-7.8%
-27.6%
-27.6%
Q3 2005
1.32
10.9%
51%
4.7%
Q4 2005
1.22
-5.5%
-20%
-7.2%
Q1 2006
1.95
59.8%
553%
51%
Q2 2006
2.33
19.5%
104%
48%
Q3 2006
2.36
1.2%
5.3%
41%
1This is a quarterly rate of return (loss). 2The rate must be taken to the 4th power to get the annualized rate. 3This is what the rate of return is if it was constant back to Q1 2005.

The headline said 70% growth, where is it in the earnings?

Seriously, time to apply the PEG ratio, using the 5 year standard that it was based on. So, being optimistic, lets say that overall annual rate of 41% will be continue over the next 5 years. Keep in mind that a 41% annual growth rate means we are looking for 1.41^5-1 = 457% over the next five years. If you don't appreciate why we are looking at 457% growth over the next 5 years, go back and read www.stockhouse.ca/blogs.asp?page=viewpost&blogID=459&postID=6959.

So P/E = $505/(2.36+2.33+1.95+1.22) = 64.2

Hmmm, 64.2 is not less than 41. 457% of sales growth over the next 5 years will not be enough. 64.2/41 = 1.56

Double hmmmm. At 1 - 1.3 the Motley fool is saying a stock is overvalued. At 1.7, it is saying short!

But, there is something even more serious to notice here, the gross rapid decline in the quarterly growth rate in 2006. The decline in that growth rate is like a nuclear melt down.

And seriously, 1.642^5-1 = 1094%. To force the PEG to be one, we need 1094% in growth of earnings over the next 5 years. And that's for the current share price to catch up to itself, without growing at this absurd rate of 450% per year. We need even more growth in real sales and real wealth if the stock continues to create market cap out of thin air.

But, given this, I predict the next headline will read an even great rate of growth. Next post I'll explain how the numbers can be used to show this, and I'll even predict when the nuclear meltdown will occur.

And even more seriously, earnings per share are 1.6% of the share price. You can do better in the bank and your money is safe.

Fantasy Girl - Googlplex^Googlplex - Part IV

Googol - 10^100

This is the 4th post in a series on valuation and growth when growth rates are big.

Recap
  • Google's 2 month growth rate on share price ($380->$505) is 210% annualized.
  • Correct use of PEG says earning must be expected to increase by 1094% in the next 5 years without any further increase in share price.
  • Quarterly data on earnings per share show dramatic declines in growth.
Perceptions of Growth - Google's Next Quarterly Report

The last quarterly headline read "Revenue Up 70%." And the next report will probably read something like "Earnings up 90%." Remember the 3 billion percent difference in annualize return between 8 and 8.1% from part 1? Yet it didn't seem so extreme using 0% and 0.1%. A large past growth rate easily hides rapidly declining growth. Here's how.

First, we need to look at earnings per share and increases in earnings per share over the previous quarter, and the quarter one year ago.



Quarter
Earnings/ share
% increase over last Quarter
% increase over Quarter 1 year earlier
Quarter increase annualized
Q4 2004
0.71
n/a
n/a
n/a
Q1 2005
1.2982%
n/a
997%
Q2 2005
1.19
-7.8%
n/a
-28%
Q3 2005
1.32
10.9%
n/a
51%
Q4 2005
1.22
-5.5%
72%
-20%
Q1 2006
1.95
59.8%
51%
552%
Q2 2006
2.33
19.5%
96%
104%
Q3 2006
2.36
1.3%
78%
5.3%

If you just compared Q3-06 to Q3-05, you'd see a 78% growth in earnings, and that's exceptional. But, where in the news was the headline:

Google's Growth in Q3 Earnings Decline by 94%

(1-1.3/19.5) * 100% = 94%

We are playing with exponential growth here, so it is fundamentally important to consider the exponential growth consequences.

But, lets look at how the headlines will read for Q4, based on 3 projections I got from MarketWatch, a low estimate of $2.31, a mean of $2.72, and a high of $3.13. Notice earnings in Q4 2005 were down. That's going to be great for punching the numbers to make things look good... Might even be able to get away with increasing projections to $1000 per share!


Q4 2006 Estimate % increase over $1.22
% increase over $2.36
Annualized Growth Rate
PEG = one @
2.31 89% -2.1%-8.2%
$795
2.72 123% 15.3%76.5%
$1150
3.13 156% 32.6%209%
$1500

So, there you have it, the next headline:

Q4 - Google's Earnings up 89%

And the red elephant hides in plain view. PEG wrongly used supports share prices at a low of $800 and a high of $1500, creating an additional $90 to 300 Billion in market cap, out of thin air. I need one of these money trees in my back yard.

But what of Q1 - 2007? Notice that jump from $1.22 to $1.95 between Q4 and Q1? That's going to play havoc with the numbers. MarketWatch estimates are a low of $2.10, a mean of $2.98 and a high of $3.28

Q1 2007 Estimate % up over $1.95
% up over $2.31
% up over $2.72
% up over $3.13
Annualized Rate Over $2.32
Annualized Rate Over $2.72Annualized Rate Over $3.13
PEG = one @
$2.10 7.7% -9.1% -23%
-33%
-32%, -65%
-80%
$73
$2.98 53% 29% 9.6%
-4.8%
176%44%
-18%
$550
$3.28 68% 42% 20.6%
4.8%
307% 111%
21%
$725

There's a lot more red elephants in that chart, and the growth over the same quarter in the previous year is much smaller than what Q4 projects. I predict there's going to be a lot of pain right about here.

One more thing, that by looking at the PEG calculation between three estimates and 2 quarters and finding a share price valuation that varies by a magnitude of TWENTY ($73 vs $1500) simply says the PEG is grossly misused and is best left for Voo Doo economics.

Part V, a different kind of valuation...

Fantasy Girl - Scrooged - Part V

"But you were always a good man of business, Jacob." Ebenezer Scrooge

Recap
  • Google's market cap: $153 billion, $38 billion created in past two month.
  • Q4 PEG could support $800-$1500 share price, creating up to $300 billion more market cap.
  • Q1/07 PEG could suggest a share price as low as $73, destroying $130 billion in market cap.
  • Oops, easy come, easy go, $6 billion of market cap gone today 11/27/06.
How does your bank treat you?

Ultimately, sound investment is about a company's ability to generate earnings relative to the investment. Sure, there is tons of money to be made on greed, fear, and speculation, but that isn't realistic or fair valuation.

Your bank:
  • Wants security for 6%
  • Good credit rating for 10%
  • Has legal recourse against you
Google, earnings per share from the last 4 quarters comes to a mere 1.6% of share price, you have no legal recourse and you are risking your savings. By banking standards, for fully secured, earnings per share needs to be in the $30/share range $7.50 per quarter at the very minimum. Currently, Google's earnings per share aren't even keeping up with the rate of inflation!

So, just how much do you expect Google to grow to reach market staturation? At some point all companies reach maturity and have limited growth prospects. Where is that for Google, and how many years?

Say the company grows to earnings of $50 per share in 10 years to reach market maturity, and at that point because Google is a big secure company, that's about where earnings will stay. This is a highly optimistic quarterly growth rate for earnings of 4.3%.

Lets examine 3 examples:
  1. You want 6% return on your money and you are confident Google can to it.
  2. For that kind of speculation, you want 10% return on your investment today.
  3. You think growing to earnings of $50/share is highly unlikely, and you want 15% because of the high risk you are taking because it is highly unlikely.
For $50/share earnings to be 6%, the share price would be $833.

% return wanted (r)
(1+r)^10 Present Value of Shares
6% 1.79 $465
10% 2.59 $321
15% 4.04 $206

So, with a low expectation of return (6%), and highly optimistic growth projections (>400%), a fair share prices would be $465. But wouldn't bonds be safer?

With a 10% expected rate of return, and a highly optimistic growth projection, $321 would be a fair share price.

And finally, if you don't think it is likely, and want 15% return because of the high risk of not making it, $206 is a fair share price.

Some created wealth is sustainable, but some is simply waiting for nuclear melt down. So Barrons called Google richly valued today.

Can we say Google Bubble?

Next a little gold dust fantasy.

www.forbes.com/2002/09/13/400fictional_5.html

Read More......

Friday, May 18, 2007

Goldcorp: The Oxymoron of Fiat Creation

Goldcorp has taught me a lot about what can be hidden in a stock. When I look at the dynamics of what drives a gold stock, the gross irony of Goldcorp is that, from my point of view, it is the epiphany of investor fears that is driving the gold bull in the first place.

So, just what are investor fears driving the gold market? The answer I get is currency devaluation due to government just printing more money. As the money supply grows, there is an escalation of inflation. The U.S. national debt is so enormous, printing money to pay bills seems more likely, so this is a serious and valid concern. Governments printing money is the cause of hyper-inflation.

Gold is supposed to be protective against this. Gold should hold its value against other currencies. This makes a certain amount of sense, however, gold stocks are not gold. They represent business that mines gold. They do not mine the gold and just sell enough to cover expenses and then save the hard asset that is supposed to protect valuation; no, they tend to sell all that they mine, paralleling the gold bug complaint that the gold that used to back currency has been sold off.

Gold companies do not print money, however, they do print stocks. Stocks are to a business what currency is to a country. If a business is printing stock, or issuing new equity, it is very comparable to government printing more money.

Just How Many Shares Has Goldcorp Printed?

The graph below show just how frivolous Goldcorp is with issuing new equity, options and warrants. Options and warrants are included and must be included to get a true picture of a company.

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If you owned say 1% of Goldcorp in 2003, well now you only own about 1/4 of one percent of the company.

Dilution is easily hidden. It can be found, but it really doesn't show up in a chart of the company's performance, like this one on Goldcorp's share price:

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A chart of a company's share price completely and utterly hides dilution. To see a true picture of performance, you really need to look at a graph of fully diluted market cap. But where do you get that? As far as I can tell, it just doesn't exist, but it is probably one of the strongest pictures of how the market is valuing a stock.

There is no way that I can go back and figure out fully diluted share/warrant/option count on a daily basis and multiply it by the share price, but, I could do it for 10 points, say at the end of each year.
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The dilution thoroughly hides the gross escalation of market cap. Seriously, this looks more like the Zimbabwe exchange than a real investment. The share price and market cap graphs look nothing alike.

There were events tied to issuing of new equity. Some was to pay back debt, much like how governments have printed currency to pay back loans. Other events were asset acquisition, such as the take over of Glamis.

The midas touch, $6 billion of fiat book value in a single deal

Glamis was a gold producing company with a good development property. Their book value in their Q3 financial report before the takeover was $2.2 billion dollars. When Goldcorp took over Glamis the cash and equity value of what they issued was $8.2 billion dollars, and Goldcorp now carries $8.2 billion dollars in assets on their books for the Glamis properties.

Essentially, Goldcorp has a hyper-inflation of asset valuation being carried on their books. As assets are mined from the ground, an appropriate allocation of book value for each mine is written off.

The hyper-inflated Glamis assets are currently mostly non-producing assets, so what is currently written down is tiny compared to the total asset picture of Goldcorp, and it is tiny compared to the relative book value that the company is carrying for all of its properties. Once these assets start producing the writing down of the fair allocation of book value of these hyper-inflated assets will implode earnings.


I find that Goldcorp is masterful at taking the focus from what ought to be the first priority for investors and and spinning impotent results into a good story. For example, look at the graph of revenue. It tells a stellar growth story, but merely looking back at the total share count suggests the revenue growth is inadequate compared to the equity growth.

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Indeed, the revenue per share has actually declined.


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Goldcorp also printed a pretty cash flow chart, again in total cash flow, and again, a pretty picture.

Photo Sharing and Video Hosting at Photobucket


But again, the per share picture isn't so pretty, it is actually down 22%.

Photo Sharing and Video Hosting at Photobucket


But not to be disuaded, I decided to look at the next "Go Goldcorp!" graph, which was earnings, and again, their presentation looks stellar.


Photo Sharing and Video Hosting at Photobucket


When you use Goldcorp's numbers for individual shareholders, it actually does look like an improvement.


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But I check calculations for myself I found $408 million in earnings when there were 703.5 million shares fully diluted did not "add" up to what they report. Practically none of the effects of share dilution and fiat book value from the Glamis merger show up in the financial reports. I took the earnings and the fully diluted share count at year end and re-plotted the data. This is ultimately what share holders are getting.

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In 2003 with 52c eps Goldcorp was trading under $16.

Goldcorp also puts its spin on gold production based on ounces for the company as a whole.

Photo Sharing and Video Hosting at Photobucket


But, what Goldcorp is producing per share is far more important. The graph below is actually per 1000 shares, and the 2007 point is projected production. Already for 2007 production has been down graded twice from 2.8 million ounces.

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The 2006 figure has totally imploded. With about $24,000 US investment you can expect to see about 2.4 ounces of gold produced. It begs the question, how can anyone possibly think that this is reasonable? If they meet their targets for 2007, the gold production per share will return to the historical levels.

Even looking at Goldcorp's Q1 financial reports you can see how they steer investors from looking at what is important in terms of their individual share ownership and direct them to the big picture of a company that is under performing on a per share basis relative to prior years. Eps for Q1 this year compared to Q1 last year were way down, but they report stellar improvement.

All in all, Goldcorp belongs to the honor role for the frivolous cap of fiat creation.

Read More......

Sunday, May 06, 2007

Low Interest Rates - As Destructive as Usury?

I was 17 when I first got a job as a teller in a credit union in 1979. This is where I first studied mortgages.

Qualifying income was such that no more than 30% of your gross income would be needed to pay the mortgage. Mortgage rates were about 10-12%. You needed qualifying income of $36,345 to qualify for $100,000 of mortgage at 10%. Most mortgages at the time were under $50,000, and people in their 30s were paying off their mortgage on their house, not a condo or a townhouse, but a house with a yard.

The credit unions had technology far ahead of the times and they had a program where I could change the variables in mortgages and view amortization tables, much like you can do today.

The changes intrigued me. I studied how much money a person could save by increasing their payments by relatively small amounts. For example, at 10% the payments on $100,000 mortgage would be about $909 per month over 25 years, and 10% was about what mortgage rates were before they spiked. Increase the payment by 10% and you would have saved 7 years, or 28% of your payments. The table below shows what happens with each 10% increase in payment.

Effects on Amortization Period of increasing payments at a fixed rate of 10%

Example A: $100,000 @ 10%
Payment Amort (months)
Months Reduced (+/- 0.5 months)
Increase in Payment - (total)
Decrease in Months to Repay - (total)
Total Interest Paid
Interest saved from last 10%*
$908.62 300 N/A
N/A N/A $172,600
N/A
$999.48 216 84
10% - (10)
28% - (28)
$115,900
$56,700
$1090.34 174 42
10% - (20)
14% - (42)
$89,700
$26,200
$1181.21 147 27
10% - (30)
9% - (51)
$73,600
$16,100
$1272.07 128 19
10% - (40)
6.3% - (57.3)
$62,800
$10,800
$1362.93
114
14
10% - (50)
4.7% - (62)
$55,400
$7,400
$1453.79
102.5
11.5
10% - (60)
3.8% - (65.8)
$49,000
$6,400
$1544.65
93.5
9
10% - (70)
3% - (68.8)
$44,400
$4,600
$1635.52
86
7.5
10% - (80)
2.5% - (71.3)
$40,700
$3,700
$1726.38
79.5
6.5
10% - (90)
2.2% - (73.5)
$37,200
$3,500
$1817.24
74
5.5
10% - (100)
1.8% - (75.3)
$34,500
$2,700
*As number of payments have been averaged to +/- 0.5 of a payment, the error in the total interest can be as much as +/- 0.25 of the payment.

The leverage of how much you could save rapidly declined as you increased payments. Where that first 10% increase brought the number of years from 25 down to 18, increasing by 20% saved an additional 3.5 years, or 14%. By increasing payments by 30%, the number of years to pay back the mortgage was cut by more than half.

Furthermore, the interest saved with that first 10% increase is enormous, 56.7% of the original mortgage amount -- about 1/3rd of the interest overall. And even more amazing, double the payment and you pay only about 1/5th the interest and can pay it off in a little over 6 years.

Effects on Payments of changing interest rates for fixed amortization

Example B: $100,000 over 300 months
Interest Rate Change in Interest Rate
PaymentIncrease/ Decrease
% Change in Payment
9%
-10%
839.14
-69.48
7.65%
9.5% -5%
873.62 -35.00
3.85%
10% 0%
908.62 0
0%
10.5% 5%
944.0935.47
3.9%
11% 10%
980.0171.39
7.86%

At those interest rates, 0.5% changes did not make huge differences to payments. When 10% is the current mortgage rate, a 1% decline or increase means the interest rate has changed by 10% (change in rate/rate*100%). The relative payment changes by less than the change in the interest rate. Interest rate increases cost more, but are manageable.

If you look at percent of that family income, a 1% increase would cost 2.36% of qualifying income. For most households income would have increased by at least that amount by the time a mortgage needed to be renewed.


Something not shown on the table is that if interest rates went down by 1%, and you kept your payment the same, the amortization would decline to 19.5 years, and you did not give up an ounce of lifestyle. If interest rates cut in half, to 5%, the amortization would decrease to 12.25 years.

The other thing I "played" with was how much would you have to change the payment to reduce amortization by a year at a time?

Effect on Payment of Reducing Amortization Period

Example C: $100,000 @ 10%
Amort (years) Monthly Payment ($)
Increase to reduce 1 year ($)
Total increase ($)
% Total increase
Total Interest Paid ($)
25 908.70 N/A N/AN/A
172,610
24 917.39 8.69 8.690.96%
164,208
23 927.18 9.79 18.482.03%
155,902
22 938.25 11.07 29.553.25%
147,697
21 950.78 12.53 42.084.63%
139,597
20 965.02 14.24 56.326.20%
131,605
19 981.26 16.24 72.567.99%
123,727
18 999.84 18.58 91.1410.0%
115,966
17 1021.21 21.37 112.5112.4%
108,327
16 1045.90 24.69 137.2015.1%
100,813
15 1074.61 28.71 165.9118.3%
93,429
14 1108.20 33.59 199.5022.0%
86,178
13
1147.85
39.65
239.15
26.3%
79,064
12
1195.08
47.23
286.38
31.5%
72,091
11
1251.99
56.91
343.29
37.8%
65,262
10
1321.51
69.52
412.81
45.4%
58,581

When interest rates were 10% small changes to a family's overall budget to increase mortgage payments brought in enormous financial reward in terms of reducing the number of years to pay back the debt - - it explains how the economic conditions enabled so many people to be paying off their mortgage in their 30s.

For simplicity, $100,000 was used, but when I first started working in the bank few mortgages were over $50,000 and I remember we were shocked when someone applied for and took out a $100,000 mortgage!

I worked in the banks through the period that interest rates doubled. There were two groups of homeowners, those that had gotten into the market recently and those who had been homeowners for a while.

It certainly made things harder for those who had been home owners for a while, but few lost their homes. For most, income had dramatically increased through the 70s, so although it hurt for that renewal period, wages had kept up enough to enable them to keep their homes.

Many who recently bought found themselves over extended and with insufficient income to cover the huge increase in mortgage payment. In Vancouver it was complicated by a housing price bubble. People who bought at the high point lost their homes, their down payments, and in some cases stilled owed money after the home was sold. In retrospect, the lucky ones failed to qualify for a mortgage.


The usurious interest rates were hard, and very, very destructive for some.

Low Interest Destructive?


Low interest rates have been looked at as a good thing for homeowners, but I beg a difference.

No question that if you owned your home, had a mortgage and interest rates decline, you gain, or if you live in a region with emigration. But what happened if you did not own your own home before interest rates declined, live in a region with population growth, and interest rate went down to 4%? First one must compare what changes on low interest rate mortgages look like.

Effects on Amortization Period of increasing payments at a fixed rate of 4%

Example D: $100,000 @ 4%
Payment Amort (months)
Months Reduced (+/- 0.5 months)
Increase in Payment - (total)
Decrease in Months to Repay - (total)
Total Interest Paid
Interest saved from last 10%
$527.84 300 N/A
N/A N/A $58,351
N/A
$580.62 257 43
10% - (10)
14.3% - (14.3)
$48,925
$9,426
$633.41 225 32
10% - (20)
10.7% - (25)
$42,199
$6726
$686.19 200 25
10% - (30)
8.3% - (33.3)
$37,142
$5,057
$738.98 181 19
10% - (40)
6.3% - (39.7)
$33,191
$3,951
$791.76
165
16
10% - (50)
5.3% - (45)
$30,016
$3,175
$844.54
151
14
10% - (60)
4.7% - (49.7)
$27,405
$2,611
$897.33
140
11
10% - (70)
3.7% - (53.3)
$25,218
$2,187
$950.11
130
10
10% - (80)
3.3% - (56.7)
$23,360
$1,858
$1002.90
122
8
10% - (90)
2.7% - (59.3)
$21,761
$1,599
$1055.68
115
7
10% - (100)
1.3% - (60.7)
$20,369
$1,394

There is no question that increasing payments reduces the interest to be paid back, but the benefit of increasing that first 10% increase in payment is about half of what it was as a percent in example A, and look at the difference in overall interest savings, $56,700 versus $9,400, about 600% more savings in interest. The leverage of what you can do to improve your economic position by increasing payments and paying is severely compromised when interest rates are low.

Doubling payments resulted in reducing the amortization to 74 months or 6 years and 2 months, but at 4% interest doubling only reduces the amortization to 115 months or 9 years and 7 months. With low interest rates when you double your payment you have to pay for an extra 41 months or 55% longer to pay off the mortgage.

Effects on Payments of changing interest rates for fixed amortization

Example E: $100,000 over 300 months
Interest Rate Change in Interest Rate
PaymentIncrease/ Decrease
% Change in Payment
3%
-25%
474.21
-53.63
10.16%
3.5% -12.5%
500.62 -27.22
5.16%
4% 0%
527.84 0
0%
4.5% 12.5%
555.8327.99
5.30%
5% 25%
584.5956.76
10.75%

The one percent increase from 4% to 5% results in the payment going up 10.8% when interest rates are low compared to 7.8% when interest rates are higher. Overall, that comes to about 3.24% of qualifying income. It does not sound like a lot, but compared to the 2.36% in example B, the overall relative increase is 37% more.

If interest rates go down to 3% and you keep your payment the same the amortization would decline to 21 years 5 months, 35% less benefit than when when interest rates were higher.

Effect on Payment of Reducing Amortization Period

Example F: $100,000 @ 4%
Amort (years) Monthly Payment ($)
Increase to reduce 1 year ($)
Total increase ($)
% Total increase
Total Interest Paid ($)
25 527.84 N/A N/AN/A
58,351
24 540.69 12.85
12.85
2.43%
55,719
23 554.75 14.06
26.91
5.10%
53,111
22 570.18 15.52
42.43
8.02%
50,527
21 587.18 16.91
59.34
11.2%
47,969
20 605.98 18.80
78.14
14.8%
45,435
19 626.87 20.89
99.03
18.8%
42,926
18 650.20 23.33
122.36
23.2%
40,443
17 676.39 26.19
148.55
28.1%
37,984
16 706.00 29.61
178.16
33.8%
35,551
15 739.69 33.69
211.85
40.1%
33,144
14 778.35 38.66
250.51
47.5%
30,762
13
823.12
44.77
295.28
55.9%
28,406
12
875.53
52.41
347.69
65.9%
26,076
11
937.67
62.14
409.83
77.6%
23,772
10
1012.45
74.78
484.61
91.8%
21,494

In the last example, to reduce the amortization period by one year you must increase the payment by 2.43%. Overall, this is an enormous difference in comparison to example C where the payment was increased by 0.96%, relatively speaking about 2.5 times as much.

The big difference is to look at the change for paying back the mortgage in 10 years. In example C if you increase the payment by 45.4% the mortgage is paid off in 10 years, where as when rates are 4% the payment has to be increased by 91.8%.

Enter Housing Costs

On the surface, lower interest rates look like win-win. On $100,000 payments start at 58% of what payments were at 10% interest, and that is an enormous savings. However, the big problem is that in many cities housing costs have increased far beyond the rate of inflation, to the point that people buying are often qualifying for their mortgage with the same parameters as those that first bought when mortgages were 10%.

There are tons of examples that could be used, but I will use what I know. In 1976, after my mother passed away, her two bedroom condo in Kitsilano lay fallow for more than a year for not being able to sell it for about $30k. In that over a year period it ate all of the equity she had built into it as well as the equity of her 3-year-old car. Indeed, when the bank foreclosed on it, her estate owed more than it had. So, $30k for a two bedroom condo in 1977 is what I know to be true.

Today the cheapest two bedroom condo I could find is priced at $379k. This represents an annual rate of return of 8.8% over the past 30 years. Minimum wage at the time was $3/hour. To put it into perspective, if minimum wage had kept up with the increase in housing cost for that period, minimum wage would be about $40/hour, but that's another issue.

To keep things simple, I'll ignore down payments, maintenance fees, property tax, etc. and just do a comparison on the two condo values.

To qualify for 30k at 10% you would have needed about $11,000 of income, or a wage of $5.64/hour. Monthly payments would be $272.61. Total amount paid would be $81,783. Interest is 63.3% of the repayment amount.

To qualify for 379k at 4% you would need $80,000 of income, or a wage of $41.03. Monthly payments would be $2,000.50. Total amount paid would be $600,150. Interest is 36.8% of the total.

On a side note, something that is utterly amazing about this to me is in 1977, as a 15-year-old, I worked part-time as a waitress and with tips I was making about $6/hour. I wonder how many 15-year-olds today could get a part-time job that would pay them $40-45/hour? In light of this enormous economic difference, no wonder so many 30 something year olds were able to pay off their mortgage!

Principal must be repaid, interest repayment is flexible

Ignoring the gross decline in wages relative to housing costs, a serious difference in the two examples is the amount of interest in the payments. By comparison, today's new buyer is grossly under privileged in their ability to get ahead by accelerating payments because the majority of the amount to be repaid is principal. When the majority was interest, that repayment could be drastically reduced by modest compromises in lifestyle.

I would further suggest that had interest rates remained higher, housing prices would be lower because less people would qualify for mortgages, and housing prices are determined by supply and demand.

So had interest rates only declined to 7% that 35-year-old $379,000 condo might be for sale for $283,000, a price that would also require $80,000 of income if interest rates were 7%, only in this case 53% would be interest. The increase in the price of the condo would still be way ahead of inflation at 7.7% per year.

If interest rates had remain in the 10% range one would only qualify for $221,000 with $80,000 of income and 63.3% of the repayment would be interest, and rate of increase in the price of the condo would be 6.9%.

Low interests rates have enabled housing prices to increase beyond reasonable levels and drastically reduced a new home owner's ability to reduce their repayment burden as most of the amount to repay is now principal.

Low interest is a function of inflation

Probably the most important disabling point for newer buyers is that low interest rates are a function of inflation. Low interest rates mean inflation is lower, which means wage increases are lower. When interest rates were high home owners could count on wage increases of 5-8% and the housing burden in their budget rapidly declined, enabling them to make far more discretionary income decisions. With low interest rates inflation is low and wage go up slowly. Indeed, many workers have experienced years with no wage increase. Increasing repayment of mortgage debt is not so easy when wages remain relatively flat.

So, Are Low Interest Rates as Destructive as Usury?

The usurious interest rates cost most people a couple hard years. Newer buyers will have a lifetime of hard years repaying their mortgages because flat wages disables them from being able to increase payments very much, if at all, and since most of the repayment amount is principal there is little power to improve financial position from leverage of increased payments. Furthermore, it isn't likely that new home owners will enjoy wealth creating due to appreciation of their home values. They have significant downside risk.

Very few who had been a home owner over 3 years lost their home from usurious interest rates of the early 80s. Housing prices doubled from the late 70s to the early 80s and it was the ones who paid the high prices who lost their homes and were left with massive debt to repay, the rest had to tighten their belts and deal with loss of lifestyle.

So, it depends on who you ask. There is no question they were a boom for people in the housing market early and that today's buyers will never enjoy the wealth creation it gave to generations before.

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